Hawth's Tools used to have a Line Metrics tool which would calculate the sinuosity. However, Hawth's tools was discontinued when ArcGIS 10 came out. It's now called the Geospatial Modelling Environment. Unfortunately, in section 5.2 (page 151) of this document, it states that the functionality is not currently available.
However, if you look at the picture which was linked to the original tool, there are instructions for how to calculate it. It shouldn't be too difficult to calculate yourself.
You say that your data is in points. You will first need to convert your points to a polyline. You can do this in ArcGIS as well in the Geospatial Modelling Environment.
You'll then want to split your polyline into line segments. You can do that with ET GeoWizard's Split Polyline Tool.
Hopefully, this will work out for you.
Just realised that the Split Polyline Tool is not a free function. Of course, you can always "Explode" the polyline in edit mode in ArcGIS.